Nuprl Lemma : gammaFIM_unfold
g,h:
List 
. a: List.
(gammaFIM(a;g;h) ~ if (||a|| =
0) then []
if (g (gammaFIM(firstn(||a|| - 1;a);g;h) @ [last(a)]) = 0) then gammaFIM(firstn(||a|| - 1;a);g;h) @ [last(a)]
else gammaFIM(firstn(||a|| - 1;a);g;h) @ [h gammaFIM(firstn(||a|| - 1;a);g;h)]
fi )
Proof
Definitions occuring in Statement :
gammaFIM: gammaFIM(a;g;h),
firstn: firstn(n;as),
length: ||as||,
append: as @ bs,
eq_int: (i = j),
ifthenelse: if b then t else f fi ,
nat: ,
all: x:A. B[x],
apply: f a,
function: x:A B[x],
subtract: n - m,
natural_number: $n,
sqequal: s ~ t,
last: last(L)
Definitions :
all: x:A. B[x],
exists: 
x:A. B[x],
member: t 
T,
ifthenelse: if b then t else f fi ,
gammaFIM: gammaFIM(a;g;h),
nat: ,
so_lambda: 
x.t[x],
implies: P 
Q,
btrue: tt,
bfalse: ff,
sq_type: SQType(T),
uall: [x:A]. B[x],
uimplies: b supposing a,
so_apply: x[s],
bool: 
,
unit: Unit,
assert: 
b,
uiff: uiff(P;Q),
and: P 
Q,
bnot: 
b,
or: P 
Q,
guard: {T},
false: False,
prop: 
,
it: 
Lemmas :
base_sq,
base_wf,
subtype_base_sq,
Error :list_wf,
nat_wf,
list_subtype_base,
set_subtype_base,
le_wf,
int_subtype_base,
Error :list_ind_reverse_unfold1,
Error :nil_wf,
eq_int_wf,
append_wf,
Error :cons_wf,
subtype_rel_set_simple,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
Error :assert-bnot,
neg_assert_of_eq_int,
length_wf,
gammaFIM_wf,
firstn_wf,
subtype_rel_dep_function,
subtype_rel_weakening,
ext-eq_weakening,
last_wf,
Error :non_null_iff_length,
subtype_rel_list,
top_wf,
subtype_top,
non_neg_length,
length_wf_nat
\mforall{}g,h:\mBbbN{} List {}\mrightarrow{} \mBbbN{}. \mforall{}a:\mBbbN{} List.
(gammaFIM(a;g;h) \msim{} if (||a|| =\msubz{} 0) then []
if (g (gammaFIM(firstn(||a|| - 1;a);g;h) @ [last(a)]) =\msubz{} 0)
then gammaFIM(firstn(||a|| - 1;a);g;h) @ [last(a)]
else gammaFIM(firstn(||a|| - 1;a);g;h) @ [h gammaFIM(firstn(||a|| - 1;a);g;h)]
fi )
Date html generated:
2013_03_20-AM-10_33_05
Last ObjectModification:
2013_03_08-PM-11_32_12
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